Help with checking Vector Question

Hey guys I am not sure if i am on the right track here so i need some advice

Question is:

if \(\displaystyle \vec{a}=3i-2j\) , \(\displaystyle \vec{b}=-4i+4j\) , and \(\displaystyle \vec{c}=6i+-9j\) express the following vectors in their simplest form:

(i)\(\displaystyle -5\vec{b}\)
(ii)\(\displaystyle 2\vec{a}-\frac{1}{2}\vec{c}\)
(iii)\(\displaystyle \frac{2}{3}\vec{a}-\frac{1}{2}\vec{b}-\frac{1}{4}\vec{c}\)

My Solution:

(i) \(\displaystyle -5\left(-4i+4j \right)=20i+\left(-20j \right)\)
(ii) \(\displaystyle 2(3i-2j)-\frac{1}{2}(6i+(-9)j)\)
\(\displaystyle = 6i-4j-3i+(-\frac{9}{2})j\)
\(\displaystyle = (6-3=3i) -4j-\frac{9}{2}\)
\(\displaystyle = -\frac{4}{1}-\frac{9}{2}\)
\(\displaystyle =-\frac{8}{2}-\frac{9}{2}\)
\(\displaystyle =-\frac{17}{2}\)

Answer? \(\displaystyle 3i-\frac{17}{2}j\)

(iii) \(\displaystyle \frac{2}{3}(3i-2j)-\frac{1}{2}(-4i+4j)-\frac{1}{4}(6i+(-9)j)\)
\(\displaystyle (2i-\frac{4}{3}j)-(-2i+2j)-(\frac{3}{2}i+(-\frac{9}{4}j)\)
\(\displaystyle 2i+2i-\frac{3}{2}i\)
\(\displaystyle = \frac{4}{1}i+\frac{3}{2}i\)
\(\displaystyle = \frac{8}{2}+\frac{3}{2}\)
\(\displaystyle =\frac{11}{2}i\)

\(\displaystyle -\frac{4}{3}j+\frac{2}{1}j-\frac{9}{4}j\)
\(\displaystyle = -\frac{16}{12}j+\frac{24}{12}j-\frac{27}{12}j\)
\(\displaystyle = -\frac{19}{12}j\)

Answer? \(\displaystyle \frac{11}{2}i-\frac{19}{12}j\)
 
Jun 2009
806
275
while removing the brackets, you have to follow the following rule.

-2(a-b) = -2a + 2b

-2(a+b) = -2a - 2b

Therefore your second the third problems are wrong. Correct it.
 
while removing the brackets, you have to follow the following rule.

-2(a-b) = -2a + 2b

-2(a+b) = -2a - 2b

Therefore your second the third problems are wrong. Correct it.
ok so (ii) answer is \(\displaystyle
3{\bf i}+(-4+\frac{9}{2}){\bf j}=3{\bf i}+\frac{1}{2}{\bf j}
\)

now i will do the (iii) one again
 

Soroban

MHF Hall of Honor
May 2006
12,028
6,341
Lexington, MA (USA)
Hello, mathematicallyretarded!

You are making hard work out of it.

This is basically Algebra I . . . combining like terms.


Given: .\(\displaystyle \begin{array}{ccc}\vec a &=&3i-2j \\ \vec b &=&-4i+4j \\ \vec c &=&6i-9j\end{array}\)

Express the following vectors in their simplest form:

\(\displaystyle (i) \;-5\vec{b}\)

\(\displaystyle -5\vec b \;\;=\;\;-5(-4i + 4j) \;\;=\;\;20i - 20j\)



\(\displaystyle (ii) \;\;2\vec a -\tfrac{1}{2}\vec c\)

\(\displaystyle 2\vec a - \tfrac{1}{2}\vec c \;\;=\;\;2(3i - 2j) - \tfrac{1}{2}(6i-9j) \)

. . . . . .\(\displaystyle =\;\;6i - 4j - 3i + \tfrac{9}{2}j\)

. . . . . .\(\displaystyle =\;\;3i + \frac{1}{2}j \)



\(\displaystyle (iii)\;\;\tfrac{2}{3}\vec a -\tfrac{1}{2}\vec b - \tfrac{1}{4}\vec c\)

\(\displaystyle \tfrac{2}{3}\vec a - \tfrac{1}{2}\vec b - \tfrac{1}{4}\vec c \;\;=\;\;\tfrac{2}{3}(3i - 2j) - \tfrac{1}{2}(-4i + 4j) - \tfrac{1}{4}(6i - 9j) \)

. . . . . . . . .\(\displaystyle =\;\;2i - \tfrac{4}{3}j + 2i - 2j - \tfrac{3}{2}i + \tfrac{9}{4}j\)

. . . . . . . . .\(\displaystyle =\;\;\frac{5}{2}i - \frac{13}{12}j \)